Eigenmodes of metallic ring systems: a rigorous approach

Summary form only given. The studies of metallic ring-like systems were stimulated by the discovery that a split ring resonator (SRR) processes a negativeu in some (microwave) frequency regimes, and thus can be employed to fabricate a left-handed meta-material. So far, the SSR and its topological equivalents were mainly studied by some empirical approaches or fully numerical calculations. The empirical approaches oversimplified the complicated local inductive/capacitive effects by some lumped elements with pre-assumed parameter values. The numerical approaches usually provide only indirect information to understand the EM properties of a SSR, such as the transmission/reflection spectra of a periodic array of SRR´s.